[tex]\it Fie\ func\c{\it t}ia\ f:\ \mathbb{R} \longrightarrow \mathbb{R},\ f(x)=ax+b.\\ \\ Determna\c{\it t}i\ a,b\in\mathbb{R},\ pentru\ care\ Gf=AB,\ unde\ A(-1,\ -7),\ B(1,\ -1)[/tex]
R :
[tex]\it A(-1,\ -7)\in Gf \Rightarrow f(-1)=-7 \Rightarrow -a+b=-7 \Rightarrow b=a-7\ \ \ \ \ (1) \\ \\ B(1,\ 1)\in Gf \Rightarrow f(1)=1 \Rightarrow a+b=1 \Rightarrow b=1-a\ \ \ \ \ (2) \\ \\ (1),(2) \Rightarrow a-7=1-a \Rightarrow a+a=1+7 \Rightarrow 2a=8 \Rightarrow a=4\ \ \ \ (3) \\ \\ (1),(3) \Rightarrow b=4-7 \Rightarrow b=-3[/tex]
